If the 8 week view is read-only (i.e. its not an input view), then yes, you can apply a user-level filter that would enable such a rolling-8-week behavior.
There are different ways to achieve the goal, here is one way:
In the 8-week (report) module, you would add user as a dimension at the module level only (i.e. omit the user dimension at the line item levels). This causes the line items to become read-only subsidiary views. You can then create a simple module that contains two line items: The first line item for Week Selector (and include the user dimension here also, no time, format this line item to Time in weeks, or perhaps just a list of numbers that represents the week numbers of the year). Then, add a 2nd line item (formatted as boolean), including the same Weeks/Time dimension as the report module) & the user dimension. Create a formula in the boolean line item that derives to TRUE if the week selected by the user matches the week of the current time period or the future 7 time periods.
Lastly, in your report module, assign the boolean line item above as a time filter based on User: Current Page... with the current page option, the filter effectively becomes user-specific.
The only nuance to this approach is that the dashboard has to be refreshed when the week is set. I prefer to guide users to the out of the box refresh option... i've seen models where a "refresh" button is included that reopens the dashboard.
The user filter line item is a boolean (it doesn't have to be boolean, but I use them more than not). For my example, I'm filtering that User Filter line item when its true. Remember, the only slightly annoying downside to this is that you have to 'refresh' the dashboard each time the filter is changed.